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Abstract

In this paper we compare experimentally two methods of detecting optical vortices from Shack-Hartmann wavefront sensor (SHWFS) data, the vortex potential and the contour sum methods. The experimental setup uses a spatial light modulator (SLM) to generate turbulent fields with vortices. In the experiment, many fields are generated and detected by a SHWFS, and data is analysed by the two vortex detection methods. We conclude that the vortex potential method is more successful in locating vortices in these fields.

The normalised intensity scintillation,
σI2, plotted against the approximate coherence length, r0, for the wavefronts used in the experiments. The error bars on the
σI2 values correspond to the maximum and minimum intensity scintillation for the various degrees of Shack-Hartmann sampling.

Graphs of the percentage of correct detection of vortices against the coherence length, r0, for the vortex potential (the blue line) and the contour sum (the red line), for the case of phase aberrations with uniform intensity. The SH sampling level is 1.68 cm/lenslet for (a), 0.83 cm/lenslet for (b), 0.55 cm/lenslet for (c) and 0.28 cm/lenslet for (d).

The percentage of correct detection of optical vortices against the coherence length, r0, and the intensity scintillation,
σI2, for the vortex potential method (blue line) and the contour sum method (red line), for the case of the full optical field. The Shack-Hartmann sampling level for each of these graphs is; 1.68 cm/lenslet for (a), 0.83 cm/lenslet for (b), 0.55 cm/lenslet for (c) and 0.28 cm/lenslet for (d).

The percentage of correct detection for the contour sum (red) and vortex potential methods (blue) against the spatial separation of vortices in terms of SH lenslets. The case of phase aberrations only, (a), and the case of the full optical field, (b), are shown for a coherence length r0 = 80 cm and an intensity scintillation
σI2=0.04.

Table 2 The data used in Fig. 4 comparing how the contour sum method performs for the case of phase aberrations only over the four SH sampling levels shown against the vortex potential method. The data highlighted in grey is that for the vortex potential method, with the data in white is the detection rate for the contour sum method.

Table 3 The data used in Fig. 4 comparing how the contour sum method performs for the full optical field case over four SH sampling levels to the vortex potential method. The data in grey is that for the vortex potential method, with the data in white is the detection rate for the contour sum method.

Metrics

Table 1

The relationship between the range of values used for the coherence length, r0, and the intensity scintillation,
σI2, in the experiments. The four separate SH lenslet samplings used are given.

Parameter

Range of Values Used

Coherence Length, r0 (cm)

80

32

21

11

8

5.7

4.7

Scintillation,
σI2

0.04

0.18

0.56

1.03

1.45

1.75

1.90

Parameter

Range of Values Used

SH Sampling (cm/lenslet)

1.68

0.83

0.55

0.28

Table 2

The data used in Fig. 4 comparing how the contour sum method performs for the case of phase aberrations only over the four SH sampling levels shown against the vortex potential method. The data highlighted in grey is that for the vortex potential method, with the data in white is the detection rate for the contour sum method.

Fried’s Parameter,r0(cm)

80

32

21

11

8

5.7

4.7

% Correct Detections

100

40

-

-

-

-

-

Sampling 1.68 cm/lenslet

65

0

-

-

-

-

-

% Correct Detections

97

73

36

24

-

-

-

Sampling 0.83 cm/lenslet

27

40

16

2

-

-

-

% Correct Detections

100

93

93

67

20

-

-

Sampling 0.55 cm/lenslet

54

44

38

11

0

-

-

% Correct Detections

100

100

100

93

87

93

73

Sampling 0.28 cm/lenslet

9

26

20

36

27

27

7

Table 3

The data used in Fig. 4 comparing how the contour sum method performs for the full optical field case over four SH sampling levels to the vortex potential method. The data in grey is that for the vortex potential method, with the data in white is the detection rate for the contour sum method.

Fried’s Parameterr0(cm)

80

32

21

11

8

5.7

4.7

Intensity Scintillation,σI2

0.04

0.18

0.56

1.03

1.45

1.75

1.90

% Correct Detections

100

50

-

-

-

-

-

Sampling 1.68 cm/lenslet

17

7

-

-

-

-

-

% Correct Detections

90

60

27

13

-

-

-

Sampling 0.83 cm/lenslet

33

40

0

0

-

-

-

% Correct Detections

100

91

53

42

7

-

-

Sampling 0.55 cm/lenslet

62

56

18

0

0

-

-

% Correct Detections

100

98

87

79

53

60

60

Sampling 0.28 cm/lenslet

4

16

33

27

13

7

0

Table 4

The data used in Fig. 8(a) for the case of phase aberrations only. It shows the percentage of correct detections of vortex pairs for various SH lenslet separations.

Average Separation (SH Lenslets)

Vortex Potential % Correct Detection

Contour Sum % Correct Detection

3.5

3

0

6.9

65

7

8.6

100

7

10.4

100

20

13.8

97

57

20.7

100

57

r0 = 80 cm and uniform intensity

Table 5

The data used in Fig. 8(b) for the case of the full optical field. The percentage of correct detections of vortex pairs for various SH lenslet separations is presented.

Average Separation (SH Lenslets)

Vortex Potential % Correct Detection

Contour Sum % Correct Detection

3.5

10

0

6.9

65

8

8.6

90

17

10.4

100

80

13.8

73

67

20.7

100

47

r0 = 80 cm and
σI2=0.04

Tables (5)

Table 1

The relationship between the range of values used for the coherence length, r0, and the intensity scintillation,
σI2, in the experiments. The four separate SH lenslet samplings used are given.

Parameter

Range of Values Used

Coherence Length, r0 (cm)

80

32

21

11

8

5.7

4.7

Scintillation,
σI2

0.04

0.18

0.56

1.03

1.45

1.75

1.90

Parameter

Range of Values Used

SH Sampling (cm/lenslet)

1.68

0.83

0.55

0.28

Table 2

The data used in Fig. 4 comparing how the contour sum method performs for the case of phase aberrations only over the four SH sampling levels shown against the vortex potential method. The data highlighted in grey is that for the vortex potential method, with the data in white is the detection rate for the contour sum method.

Fried’s Parameter,r0(cm)

80

32

21

11

8

5.7

4.7

% Correct Detections

100

40

-

-

-

-

-

Sampling 1.68 cm/lenslet

65

0

-

-

-

-

-

% Correct Detections

97

73

36

24

-

-

-

Sampling 0.83 cm/lenslet

27

40

16

2

-

-

-

% Correct Detections

100

93

93

67

20

-

-

Sampling 0.55 cm/lenslet

54

44

38

11

0

-

-

% Correct Detections

100

100

100

93

87

93

73

Sampling 0.28 cm/lenslet

9

26

20

36

27

27

7

Table 3

The data used in Fig. 4 comparing how the contour sum method performs for the full optical field case over four SH sampling levels to the vortex potential method. The data in grey is that for the vortex potential method, with the data in white is the detection rate for the contour sum method.

Fried’s Parameterr0(cm)

80

32

21

11

8

5.7

4.7

Intensity Scintillation,σI2

0.04

0.18

0.56

1.03

1.45

1.75

1.90

% Correct Detections

100

50

-

-

-

-

-

Sampling 1.68 cm/lenslet

17

7

-

-

-

-

-

% Correct Detections

90

60

27

13

-

-

-

Sampling 0.83 cm/lenslet

33

40

0

0

-

-

-

% Correct Detections

100

91

53

42

7

-

-

Sampling 0.55 cm/lenslet

62

56

18

0

0

-

-

% Correct Detections

100

98

87

79

53

60

60

Sampling 0.28 cm/lenslet

4

16

33

27

13

7

0

Table 4

The data used in Fig. 8(a) for the case of phase aberrations only. It shows the percentage of correct detections of vortex pairs for various SH lenslet separations.

Average Separation (SH Lenslets)

Vortex Potential % Correct Detection

Contour Sum % Correct Detection

3.5

3

0

6.9

65

7

8.6

100

7

10.4

100

20

13.8

97

57

20.7

100

57

r0 = 80 cm and uniform intensity

Table 5

The data used in Fig. 8(b) for the case of the full optical field. The percentage of correct detections of vortex pairs for various SH lenslet separations is presented.